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Molecular Calculation of the Critical Parameters of Classical Helium



Richard A. Messerly, Navneeth Gokul, Andrew J. Schultz, David A. Kofke, Allan H. Harvey


We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh virial and find the conditions where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor- liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K as measured for real helium), the critical pressure is 0.93 MPa, and the critical density is 28-30 mol/L. The effect of three-body forces on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at temperatures where quantum effects are expected to be negligible (such as most gas-processing operations); in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.
Journal of Chemical and Engineering Data


critical parameters, Gibbs ensemble simulation, helium, nuclear quantum effects, thermodynamic properties, virial coefficients


Messerly, R. , Gokul, N. , Schultz, A. , Kofke, D. and Harvey, A. (2019), Molecular Calculation of the Critical Parameters of Classical Helium, Journal of Chemical and Engineering Data, [online],, (Accessed April 20, 2024)
Created July 1, 2019, Updated October 12, 2021